Where is today's equivalent of Dr Heath of Eton who, in 1736, retired to bed for a week with strained muscles after giving seventy boys ten strokes each?

The tough, outdoors spirit survived long after that. As recently as the 1950s, Cheltenham Ladies' College girls were required to lift their skirts on a midwinter parade to check they were wearing the regulation school knickers.

Would parents flock to independent schools if more of them could afford it?

Now, rather than promoting their character-forming Spartan surroundings, the public schools like to emphasise their modern facilities, flexible boarding arrangements, liberal views and their freedom from social elitism.

Like any commercial survivor, the independent schools have been very adept at reinventing themselves.

As mere tradition and social exclusivity lost its appeal, the independent sector's unique selling points became small classes and good exam results.

Instead of appealing to the sons of "old boys" they now gear their marketing to so-called "first-time buyers" - parents who were not themselves educated privately.

More youngsters

The latest annual census from the Independent Schools Information Service shows pupil numbers have risen for the sixth successive year. This year's increase was 1.4%.

But what is interesting is the variation in popularity of independent education for children of different ages.

Following the pattern of recent years, the biggest increase has been for the youngest pupils. So nursery numbers (ages two to four) are up by 2.5%. By contrast, sixth-form numbers are up by just 0.4%.

This reflects the weak recruitment into independent schools in the early 1990s. That age group is now moving into the sixth form. Last year, for example, the numbers in independent sixth forms fell by 2%.

In terms of "market share", the past decade has been a period of stagnation, even decline, for independent schools.

In 1991, they educated 6.8% of all children of compulsory school age. This fell in successive years until it was down to 6.0% by 1996. It has stayed at this level in each of the past five years.

On the up

However, since the growth in numbers of recent years has been among the youngest age groups it seems likely that, providing these children stay in the private sector, its "market share" may start to rise again.

So what causes this fluctuating popularity? Is it about the positive appeal of the independent schools or is it more to do with negative factors which frighten parents from the state system?

Let's look at two recent periods when private school recruitment fell: The early 1980s and the start of the 1990s.

Was the first of these dips the result of parents recovering from the reorganisation turmoil of the 1970s and enthusing about comprehensive schools?

In the early 1990s were parents turning back to the state system because of an enthusiasm for the national curriculum?

Sadly for those who would like to believe that if state schools are good enough the private system will become unnecessary, it is probably nothing to do with these factors.

The explanation is much simpler: Recruitment falls at times of economic recession when middle-class incomes are squeezed.

Rising fees

So, would parents flock to independent schools if more of them could afford it? Whether state school supporters like it or not, opinion polls suggest that almost half of parents would.

However, the independent sector continues to price many parents out of the market.

School fees have been rising with the rapidity and regularity of Premiership football admission prices.

Like the soccer clubs, they have not yet felt the pinch, although they may be stretching the patience of loyal supporters

School fees rose this year by an average of 6.7%, roughly double the rate of inflation. This is not unusual. Fees have risen by more than both the retail prices index and average earnings in all but one of the past 10 years.

The steady rise in fees means spending per pupil in the private sector is now roughly double the level in state schools. When Tony Blair promised recently that his long-term target was to ensure state schools were as well funded as private schools he was setting his sights very high indeed.

Treading water

The overall picture for the independent sector is pretty healthy.

It has proved to be remarkably flexible, able to reinvent itself for changing parental taste.

A number-crunching projection by the government suggests the independent sector will increase its market share by around 0.4% over the next decade.

But independent schools should not be complacent. That modest growth would merely take them back to where they were seven years ago.

We also appear to be on the verge of another recession. If fees continue to rise, will the recent recruits to pre-prep and prep schools stay with the private sector?

If these changes were to coincide with growing confidence in state schools - primary class sizes are now smaller, the literacy and numeracy hours appear to be popular with parents, and school spending is now rising in real terms - then the private sector will, once again, have to reinvent itself.